A dart leaves the barrel of a blowgun at a speed v. The length of the blowgun barrel is L. Assume that the acceleration of the dart in the barrel is uniform.
a) Show that the dart moves inside the barrel for a time of 2L/v
Express your answer in terms of the variables L and v.
b) If the dart's exit speed is 15.0 m/s and the length of the blowgun is 1.4 m, show that the time the dart is in the barrel is 0.19 s.Express your answer with the appropriate units
please help me on units
d = ut + 1/2 * at^2
d = 0 + 1/2 * (v/t) * t^2
2d = vt
2d/v = t
d = L
2l/v =t
To solve these questions, we can use the concepts of distance, speed, time, and acceleration.
a) The first step is to determine the time it takes for the dart to travel the length of the blowgun barrel. We know that the distance traveled, d, is equal to the length of the blowgun barrel, L. We also know the speed, v, at which the dart leaves the barrel.
The equation we can use to relate distance, speed, and time is:
d = v * t
Substituting the known values, we have:
L = v * t
Now, we can rearrange the equation to solve for time, t:
t = L / v
Therefore, we have shown that the dart moves inside the barrel for a time of 2L/v by multiplying the expression for time, t, by 2:
2 * t = 2L / v
b) In this part, we are given additional information: the exit speed of the dart is 15.0 m/s, and the length of the blowgun barrel is 1.4 m. Let's calculate the time the dart is in the barrel using the equation derived above:
t = L / v
Substituting the given values, we have:
t = 1.4 m / 15.0 m/s
To ensure that the units are consistent, we divide 1.4 m by 15.0 m/s:
t ≈ 0.0933 s
However, this time corresponds to the time it takes for the dart to travel through half of the blowgun barrel. To find the total time the dart spends inside the barrel, we multiply the time by 2:
2 * t ≈ 2 * 0.0933 s
2 * t ≈ 0.1866 s
Now, the time the dart is in the barrel is approximately 0.19 s (rounded to two decimal places), with the appropriate units of seconds.